19 of the Russian's 21 titles have been won on hardcourt
A resurgent the Russian player won his maiden trophy for over two years with victory over opponent Moutet in the competition final.
The Russian, a ex- world number one, has endured a torrid period, achieving just a single victory at the Grand Slams and suffering a meltdown at the American major.
Medvedev's inconsistency on the tennis tour - and difficulties with his serving in particular - led to him dropping out of the top ten and ultimately separating with long-term mentor his previous coach.
Currently training with Thomas Johansson and Goetzke, he has steadily progressed in the past month - peaking in a closely contested three-set victory over challenger Moutet.
This represents his maiden championship after the Rome competition and first on a hard surface after that period of that year.
Success also signifies the Russian has won 21 victories at 21 distinct competitions.
"This marks the first occasion I'm at a event with my both daughters at once, so to secure a title is really nice," said world number 14 Daniil Medvedev.
"This victory is in honour of my second daughter her name, because the initial championship I got when my first daughter her name was born was for her."
Medvedev, the former major winner, had failed in his previous six championship matches, comprising in that event in the past months.
His retrieving strategy and frequent outbursts on court had led observers to doubt if his capacity to compete at the highest level was finished.
Yet the player has made changes in recent weeks, making an effort to approach the net and compete positively, supported by an improved service.
The champion recovered from a disadvantage in the first set against the tricky opponent, securing 4 of the last five exchanges to gain the advantage.
The pair traded break points in the second set before the challenger, striving for his initial ATP Tour victory, took control to create a decider.
The opponent defended four initial chances in a close deciding set before Medvedev broke to fifteen to serve for the match.
Fittingly, the winner earned the win with a point at the net area, with the Frenchman failing to control a volley after over two and a half hours.